At 55°, this angle is acute, meaning it is narrower than the corner of a square. It is more than half of a right angle. Add 35° more and you get a square corner.
55° is 11/72 of a full circle, or 11π/36 radians. If you face north and turn 55° clockwise, you end up facing between NE and ENE (closest to northeast (NE)).
55° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 35° |
| Supplement (adds to 180°) | 125° |
| Explement (adds to 360°) | 305° |
| Radians | 11π/36 ≈ 0.959931 |
| Gradians | 61.1111 grad |
| Fraction of a turn | 11/72 (15.28%) |
| Degrees, minutes, seconds | 55° 0′ 0″ |
| Slope (grade) | 142.81% |
| Roof pitch | 17.14/12 |
| Compass bearing | between NE and ENE (closest to northeast (NE)) |
Trigonometric values of 55°
| Function | Value |
|---|---|
| sin 55° | 0.819152 |
| cos 55° | 0.573576 |
| tan 55° | 1.428148 |
55° on a protractor
How to draw a 55° angle with a protractor
- Draw a straight line with a ruler. This is the first arm; mark the vertex at one end.
- Place the center mark of the protractor exactly on the vertex and line up the 0° baseline with your line.
- Find 55° on the row of numbers that reads 0° on your line (protractors have two rows running in opposite directions) and make a small dot at the edge.
- Remove the protractor and draw a line from the vertex through the dot. Mark the angle with an arc and label it 55°.
Drawing it a 55° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 7 inches (about 7″) along it from the vertex.
- At that mark, draw a line straight up at 90° and measure exactly 10 inches up it.
- Join the top mark to the vertex. The angle at the vertex is 55°, because tan 55° ≈ 1.4281.
Where you see 55° angles
- A 17/12 roof pitch is 54.78°, very close to 55°.
- A board sloped at 55° rises about 171.4 inches over a 10-foot (120-inch) run.
- 55° of latitude on Earth spans roughly 3,798 miles north to south.
- The Earth turns 55° on its axis in about 3 h 40 min.
Related angles
55° angle FAQ
What type of angle is 55°?
A 55° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 55°?
The complement of 55° is 35° (together they make 90°), and the supplement is 125° (together they make 180°).
How many radians is 55 degrees?
55° = 11π/36 radians ≈ 0.9599 rad. To convert degrees to radians, multiply by π/180: 55 × π/180 = 11π/36.
What is 55° as a slope or roof pitch?
55° is a 142.8% slope, which is a roof pitch of 17.14/12 (a rise of about 17 1/8 inches for every 12 inches of run).
